We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space.
arXiv:2609.00372v1 Announce Type: cross
Abstract: With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data---that is, coherently rathe...
By Robin Lorenz, Eric Brunner, Marcello Benedetti
The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds only weak pointwise similarity between mo...
arXiv:2609.24209v1 Announce Type: new
Abstract: The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent wor...
By Chenming Shang, Yujin Tang, Jun Jie Ou Yang, Ruize Xu, Adam Breuer, Nikhil Singh
The paper introduces the Lattice Representation Hypothesis (LRH) to explain why different alignment criteria—such as neighbor overlap, spanning trees, and distances—yield varying views on model representation convergence. It shows that the Platonic Representation Hypothesis (PRH) reflects agreement at the top of a lattice, while evidence comes from criteria near the bottom, and that the Aristotelian Representation Hypothesis (ARH) limits convergence to local neighborhoods due to calibration effects. Experiments on numerous pretrained vision and language models, along with theoretical analyses of linear autoencoders and contrastive Gibbs models, support the LRH’s claim that training procedures and objectives determine which criteria are reliably met across runs.
By Dai Shi, Andi Han, Xiaoyu Li, Luke Thompson, Jos\'e Miguel Hern\'andez-Lobato
The paper develops a finite‑measurement framework for inferring the symmetry group that a quantum learning model should respect, based on candidate transformations and limited data. It shows that observable‑invisible transformations correspond to the stabilizer of a projected state when the probe span is invariant, and that recovered generators form a valid subgroup with a continuous invisible space identified via its Lie algebra. The authors introduce an unbiased shadow statistic that improves estimation rates, establish optimal gap dependence through a commuting‑qubit lower bound, and provide tools for task validation, bias quantification, and capacity analysis, all illustrated with Ising‑chain calculations.
By Zeyu Chen
arXiv:2601. 18930v4 Announce Type: replace-cross Abstract: We are interested in enabling autonomous agents to learn and reason about systems with hidden states, such as locking mechanisms.
By Seiji Shaw, Travis Manderson, Chad Kessens, Nicholas Roy
The paper derives an information‑theoretic bound for a shared‑state cognitive architecture that uses an auxiliary variable to mediate context. It shows that the residual dependence of observable behavior on context, given the shared state, is bounded by the information carried by the auxiliary variable and its conditional entropy. A recognition‑memory example illustrates how to compute and compare this bound across different representational choices, providing a framework for analyzing context‑memory‑control trade‑offs in cognitive models and artificial agents.
By Song-Ju Kim
The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.
The paper studies when joint-embedding predictive architectures (JEPAs) can recover underlying causal states from high‑dimensional observations. It introduces a latent variable model where observations arise from causal states with action‑conditioned dynamics, and proposes an information‑theoretic objective that maximizes conditional likelihood while preserving state entropy. The authors prove identifiability conditions—particularly sufficient action‑induced variation—and instantiate the objective as an action‑modulated Gaussian additive‑noise model (A‑JEPA), demonstrating theoretical and empirical success in synthetic and visual benchmarks.
By Yuhang Liu, Zhuo Huang, Javen Qinfeng Shi
arXiv:2606. 01092v1 Announce Type: cross Abstract: Supervised learning evaluates predictors through their input-output behavior.
By Vasileios Sevetlidis
The paper introduces the Bayesian Mirror Architecture (BMA), a self-referential generative model where sensory abstractions, meta-abstractions, and a self-latent interact through a closed update loop, binding self-representations to abstract world models. Consciousness is defined as an architectural property of this circular structure rather than an optimization goal, with inference occurring over probability measures in an optimal-transport space. Stability, coherence, and causal learning are formalized using the 2‑Wasserstein metric, leading to concepts such as self-manifolds, Wasserstein epsilon-necks, and a Causal Learning Regime that diagnoses learnable causal structure without implying consciousness.
By Eduardo Righi Capanema de Almeida